So I've been hunting after a vintage Conquest for a while, and it looks like I've found my watch. Now, she's a little bit beat, but from what I can see, she appears to be mostly there. From my research, I believe it to be a Reference 9020, Longines Contquest Automatic-Date. This would mean it's housing a Cal. 291, and was produced between 1959-1961. As for it's issues - it appears that the crown is wrong (and I've had no luck finding out what crown it's supposed to have), and I'm very suspect about the hands - the second hand is very wrong, but I have mixed feelings about the minute and hour hand. The strap and buckle is wrong, but that's relatively easy to source/fix. Any thoughts?
The dial is correct and that would definitely have a 291 inside. The hour & minute hands look authentic too. The crown should be the scalloped version like this: as shown in this thread: http://omegaforums.net/threads/a-question-of-conquest-crown.20390/
You might want to check this out too: http://omegaforums.net/threads/homemade-conquest-crown-–-will-it-work.14878/